Lecture 5
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"ename": "ValueError",
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"evalue": "shapes (300,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m/tmp/ipykernel_21709/3680822285.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[0mdense1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLayer_Dense\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;31m# Perform a forward pass of our training data through this layer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m \u001b[0mdense1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mforward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 25\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/tmp/ipykernel_21709/3680822285.py\u001b[0m in \u001b[0;36mforward\u001b[0;34m(self, inputs)\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mforward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;31m# Calculate output values from inputs, weights and biases\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweights\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbiases\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;31m# Create dataset\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m~/.local/lib/python3.10/site-packages/nnfs/core.py\u001b[0m in \u001b[0;36mdot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0morig_dot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0morig_dot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'float64'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'float32'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 23\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m~/.local/lib/python3.10/site-packages/nnfs/core.py\u001b[0m in \u001b[0;36mdot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0morig_dot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0morig_dot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'float64'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'float32'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 23\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mValueError\u001b[0m: shapes (300,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)"
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[ 0.0000000e+00 0.0000000e+00 0.0000000e+00]\n",
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" [-1.0475188e-04 1.1395361e-04 -4.7983500e-05]\n",
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" [-2.7414842e-04 3.1729150e-04 -8.6921798e-05]\n",
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" [-4.2188365e-04 5.2666257e-04 -5.5912682e-05]\n",
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" [-5.7707680e-04 7.1401405e-04 -8.9430439e-05]]\n"
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]
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}
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],
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@ -269,6 +269,146 @@
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"print(dense1.output[:5])\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Python Array Summation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"45\n",
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"[12 15 18]\n",
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"[ 6 15 24]\n",
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"[[12 15 18]]\n",
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"[[ 6]\n",
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" [15]\n",
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" [24]]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
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"A = [\n",
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" [1, 2, 3],\n",
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" [4, 5, 6],\n",
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" [7, 8, 9]\n",
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"]\n",
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"\n",
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"# Sum the elements in the array resulting in a scalar\n",
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"print(np.sum(A))\n",
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"\n",
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"# Sum the rows resulting in a row vector\n",
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"'''\n",
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" [1, 2, 3]\n",
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"+ [4, 5, 6]\n",
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"+ [7, 8, 9]\n",
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"= [12, 15, 18]\n",
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"'''\n",
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"print(np.sum(A, axis=0))\n",
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"\n",
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"# Sum the columns resulting in a column vector\n",
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"'''\n",
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"1 + 2 + 3 = 6\n",
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"4 + 5 + 6 = 15\n",
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"7 + 8 + 9 = 24\n",
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"'''\n",
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"print(np.sum(A, axis=1))\n",
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"\n",
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"# keepdims will keep the dimension of A\n",
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"print(np.sum(A, axis=0, keepdims=True))\n",
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"print(np.sum(A, axis=1, keepdims=True))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Python Array Broadcasting Rules\n",
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"Check if arrays are broadcastable by scanning right to left for their dimensions. If they share the sime size in that dimension, either of them is size 1, or one size does not exist, continue left.\n",
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"\n",
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"Given A is 3x3 and B is 3x3, check if it is broadcastable.\n",
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"\n",
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"3 x 3\n",
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"\n",
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"3 x 1\n",
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"\n",
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"Start by comparing 3 and 1. This is fine because B has size 1.\n",
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"\n",
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"Move to 3 and 3. This is fine because they are equal. The arrays are broadcastable.\n",
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"\n",
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"Once the arrays are deemed broadcastable, Python will maniupulate one or the other to perform the operation."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[ 2 3 4]\n",
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" [ 6 7 8]\n",
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" [10 11 12]]\n",
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"[[ 2 3 4]\n",
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" [ 6 7 8]\n",
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" [10 11 12]]\n",
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"[[-2 -1 0]\n",
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" [-2 -1 0]\n",
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" [-2 -1 0]]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
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"A = np.array([\n",
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" [1, 2, 3],\n",
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" [4, 5, 6],\n",
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" [7, 8, 9]\n",
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"]) # 3 x 3\n",
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"\n",
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"B = np.array([\n",
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" [1],\n",
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" [2],\n",
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" [3]\n",
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"]) # 3 x 1\n",
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"\n",
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"print(A+B)\n",
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"\n",
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"# Adding the arrays will broadcast B into a 3x3 in order to add them.\n",
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"B_broadcast = np.array([\n",
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" [1, 1, 1],\n",
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" [2, 2, 2],\n",
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" [3, 3, 3]\n",
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"]) # 3 x 1\n",
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"\n",
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"print(A+B_broadcast)\n",
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"\n",
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"# Example\n",
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"# Take each row and subtract the maximum value from the row\n",
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"A = np.array([\n",
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" [1, 2, 3],\n",
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" [4, 5, 6],\n",
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" [7, 8, 9]\n",
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"]) # 3 x 3\n",
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"\n",
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"# Gets the max value in each row by comparing columns (axis1). Use keepdims so it is a column vector\n",
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"result = A - np.max(A, axis=1, keepdims=True)\n",
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"print(result)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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Binary file not shown.
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print(dense1.output[:5])
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# %% [markdown]
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# # Python Array Summation
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# %%
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import numpy as np
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A = [
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[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]
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]
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# Sum the elements in the array resulting in a scalar
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print(np.sum(A))
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# Sum the rows resulting in a row vector
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'''
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[1, 2, 3]
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+ [4, 5, 6]
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+ [7, 8, 9]
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= [12, 15, 18]
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'''
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print(np.sum(A, axis=0))
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# Sum the columns resulting in a column vector
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'''
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1 + 2 + 3 = 6
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4 + 5 + 6 = 15
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7 + 8 + 9 = 24
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'''
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print(np.sum(A, axis=1))
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# keepdims will keep the dimension of A
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print(np.sum(A, axis=0, keepdims=True))
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print(np.sum(A, axis=1, keepdims=True))
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# %% [markdown]
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# # Python Array Broadcasting Rules
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# Check if arrays are broadcastable by scanning right to left for their dimensions. If they share the sime size in that dimension, either of them is size 1, or one size does not exist, continue left.
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#
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# Given A is 3x3 and B is 3x3, check if it is broadcastable.
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#
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# 3 x 3
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#
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# 3 x 1
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#
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# Start by comparing 3 and 1. This is fine because B has size 1.
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#
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# Move to 3 and 3. This is fine because they are equal. The arrays are broadcastable.
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#
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# Once the arrays are deemed broadcastable, Python will maniupulate one or the other to perform the operation.
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# %%
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import numpy as np
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A = np.array([
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[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]
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]) # 3 x 3
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B = np.array([
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[1],
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[2],
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[3]
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]) # 3 x 1
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print(A+B)
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# Adding the arrays will broadcast B into a 3x3 in order to add them.
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B_broadcast = np.array([
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[1, 1, 1],
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[2, 2, 2],
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[3, 3, 3]
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]) # 3 x 1
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print(A+B_broadcast)
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# Example
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# Take each row and subtract the maximum value from the row
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A = np.array([
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[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]
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]) # 3 x 3
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# Gets the max value in each row by comparing the columns (axis1). Use keepdims so it is a column vector
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result = A - np.max(A, axis=1, keepdims=True)
|
||||
print(result)
|
||||
|
||||
|
||||
# %% [markdown]
|
||||
# # Activation Function: ReLU
|
||||
# Rectified Linear Unit
|
||||
|
||||
Loading…
Reference in New Issue
Block a user